Why can't anything go faster than the speed of light? In order to figure out why the speed of light is the maximum limit of speed of the universe,
we must figure out how motion through space affects length, momentum, and the energy of moving objects. First there is the subject of length contraction, then there is momentum, inertia, mass and energy, kinetic energy, and the correspondence principle. All of these will explain why nothing can surpass the speed of light. What it takes is all of these factors that work together to create what we know as the "universal speed limit". Each element has its own specific and important job of the matter. It's thanks to the brilliant scientists such as the astronomical Galileo, the core rule maker Issac Newton, and the world's most well known scientist Albert Einstein. These scientists made breakthroughs that impacted science and its progress forever. Albert Einstein is believed to have the greatest of impact on these subjects still, for special relativity itself was introduced by him. What Einstein's formula describes is the motion of things traveling and speeds close to the speed of light. Newton set the base for this formula. All Einstein did was build on it. The difference between Einstein's theory and Newton's theory for motion is minute and Einstein's corrections should not take away from Newton's findings. So here we go into only a small part of the journey that is special relativity. (1)(7)
Vocabulary
Relativistic Momentum- momentum at high speeds that is approaching the speed of light
Rest Mass- the intrinsic mass of an object, a fixed property independant of speed or energy
Rest Energy- E=mc^2, "the energy of being"
Time- finite duration
Length Contraction- "shortening" of length
Impulse- applied force on an object
Inertia- the resistance to changes in motion
Velocity- the rapidity of motion
Mass- a body of coherent matter
Energy- unseen activity
Length Contraction
We realize that time is relative, but not many know that length is relative also. It all depends on at what speed the object is moving, and get this, as the objects gets faster and faster the object actually contracts in length! Albert Einstein theorized that the length of objects that are moving at relativistic speeds undergo a contraction along the dimension of motion. Basically, as the object's speed gets closer to the speed of light, the shorter in length it appears. So if there is an object at rest that is measured to be 200 meters long, that same object would be measured less than 200
Albert Einstein
meters long if moving at relativistic speeds. This is not because of faulty skills of whomever or what ever is measuring it, it is just that the object has contracted in length due to the stationary reference frame. Here is an animation that will visually aid you in this phenomenon:
Spaceship Moving at 10 % the Speed of Light:
Spaceship moving at 86.5% the Speed of Light: Spaceship Moving at the 99 % the Speed of Light:
Spaceship moving at 99.99% the Speed of Light:
Image courtesy of The Physics Classroom
As you can see, the spaceship becomes measurable shorter in length as is travels closer and closer to the speed of light.
But all of this depends on the point of view also. The length appears to be contracted when the viewpoint is parallel to the motion of the object. There is a formula for this phenomenon: L = L0((1 - v2/c2))1/2 In this formula L is the other observer, L0 is the observer in the reference frame, v is the speed of the object, and c is the speed of light in a vacuum. Part of this formula is used for others as well, as you will see in the next section when they are calculating momentum and its limits. To explain the formula, its like the difference of the perspective of an observer on earth looking at a moving rocket ship and a person who is actually in the rocket. They will both measure it differently because of their view points, and you would use the L = L0((1 - v2/c2))1/2 and plug in the known measurement in its correct spot in order to aquire the other observers measurement. (1)(2)(9)(10)(7)
Momentum
Also there is the element of momentum and inertia in relativity. Momentum is like when one pushes an object. If we push a freely moving object then it will accelerate, and if the push is steady then it will go faster and faster, and if there is a great force pushing on the object then we expect the speed of the object to increase. So why can't anything go past the speed limit of the speed of light? Well the fact is that there is no possible way to create such a force to even reach the speed of light. Newtons 2nd Law has to do with momentum and
Young Isaac Newton
it involves Newton's formula: p=Fv, but to Newton this meant infinite momentum which cannot be so in relativity, so Einstein placed the formula: the square root of 1-(v^2/c^2). So Newton modified his formula to make it relativistic. One finds out that to reach the speed of light an object would have to have infinite momentum and that means that there would aso have to be an infinite amount of force that is on the object, therefore it is concluded that the object will always move at speeds less than the speed of light. Momentum is like kenetic energy in the aspect that they both grow rapidly as the speed inclines. Here is a formula that illustrates this action:. Though it can progressively get closer to the speed of light, it will never surpass it. As it has been said, impulse, or the applied force on an object, affects momentum. Just like in football when a runner and tackler meet.
Football and Physics
The photograph on the left illustrates this in action. When the momentum of the two are equal, they both will come to a complete stop at the point of their collision. But lets say the ball carrier has more momentum than the tackler. Then the ball carrier is able to knock the tackler back with an amount of force that is equal to the difference in their momentum, then the carrier will accelerate as he regains his clear path.(2)(4)(5)(8)
Inertia
Newton's first law of motion is known as the law of inertia, where inertia is a property of matter that opposes changes in velocity. Inertia causes a mass to stay at rest or in motion unless disturbed by another force. For example, if something is going at a steady and constant speed in a straight line, then it will not spontaneously change direction, speed up, or slow down on its own. The object would have to be disturbed by another force, and just like the inertia man, if it is standing still it will continue to do so. Inertia is the resistance in changes of motion. Let's say there is a small object and bigger heavier object. If the same amount of force is exerted on them, the bigger object's path of motion, it will be less affected than that of the small object. the difference between inertia and momentum is that inertia is a property of mass and does not change, and momentum is what changes as an object changes its velocity. We also have to remember that even though it takes pushes and pulls to change to change an object's velocity, it does not require pushes and pulls for the object to remain in motion, for the object has the ability to move on its own. Galileo is the first to consider this concept. He had formed the main theory of defining the causes of motion before Sir Issac Newton adapted his theory and finalized it by making it into a law. Lets say you are pushing a chair. It is automatically thought that when you stop pushing the chair, it will stop moving, but it was Galileo who believed that even as the force of your push is taken away from the chair, it will still maintain its velocity and continue to move across the room. Actually it is for certain that it will, but only if it is left alone (11)(12)
Equivalence of Mass and Energy
The more remarkable part of Albert Einstein's special theory of relativity is his conclusion that mass is merely a type of energy and is called the Law of Conservation of Mass-Energy. In his discoveries, Einstein found that energy equals mass multiplied by the speed of light squared. This equation is often his most well known and is written as E=mc2. Where E stands for energy, m and c stand for mass and the speed of light respectively. Mass that turns into forms of energy is just a tiny percentage of what is the total mass that is out of our sensory range. For example, if there is a chemical reaction, the mass and energy really appear to be conserved separately, but in a nuclear reaction the energy that is released is often around a million times greater than in a chemical one. In this the change in mass is easily measured. Mass refers to the total number of atoms that make up any object that is composed of matter. Weight is the rate at which gravity exerts force on that mass and can fluctuate depending on the location, whereas mass is constant. There is a strong difference between enrgy and mass even though the two are closely related and often dependent on the other. Mass is tangible, you can see, pick up, and feel it; however, energy is more abstract . It is often defined as "the ability to do work". Even in an object with a small mass, there is a massive amount of energy. The Law of Conservation of Mass/Energy states that the two are interchangible. For example, mass can be turned into energy and visa-versa. It was this very principle that created the first nuclear bomb.
Special Relativity- Length, Momentum, and Energy
Table of Contents
we must figure out how motion through space affects length, momentum, and the energy of moving objects. First there is the subject of length contraction, then there is momentum, inertia, mass and energy, kinetic energy, and the correspondence principle. All of these will explain why nothing can surpass the speed of light. What it takes is all of these factors that work together to create what we know as the "universal speed limit". Each element has its own specific and important job of the matter. It's thanks to the brilliant scientists such as the astronomical Galileo, the core rule maker Issac Newton, and the world's most well known scientist Albert Einstein. These scientists made breakthroughs that impacted science and its progress forever. Albert Einstein is believed to have the greatest of impact on these subjects still, for special relativity itself was introduced by him. What Einstein's formula describes is the motion of things traveling and speeds close to the speed of light. Newton set the base for this formula. All Einstein did was build on it. The difference between Einstein's theory and Newton's theory for motion is minute and Einstein's corrections should not take away from Newton's findings. So here we go into only a small part of the journey that is special relativity. (1)(7)
Vocabulary
Length Contraction
We realize that time is relative, but not many know that length is relative also. It all depends on at what speed the object is moving, and get this, as the objects gets faster and faster the object actually contracts in length! Albert Einstein theorized that the length of objects that are moving at relativistic speeds undergo a contraction along the dimension of motion. Basically, as the object's speed gets closer to the speed of light, the shorter in length it appears. So if there is an object at rest that is measured to be 200 meters long, that same object would be measured less than 200
Spaceship Moving at 10 % the Speed of Light:
Spaceship moving at 86.5% the Speed of Light:
Spaceship Moving at the 99 % the Speed of Light:
Spaceship moving at 99.99% the Speed of Light:
As you can see, the spaceship becomes measurable shorter in length as is travels closer and closer to the speed of light.
But all of this depends on the point of view also. The length appears to be contracted when the viewpoint is parallel to the motion of the object. There is a formula for this phenomenon:
L = L0((1 - v2/c2))1/2 In this formula L is the other observer, L0 is the observer in the reference frame, v is the speed of the object, and c is the speed of light in a vacuum. Part of this formula is used for others as well, as you will see in the next section when they are calculating momentum and its limits. To explain the formula, its like the difference of the perspective of an observer on earth looking at a moving rocket ship and a person who is actually in the rocket. They will both measure it differently because of their view points, and you would use the L = L0((1 - v2/c2))1/2 and plug in the known measurement in its correct spot in order to aquire the other observers measurement. (1)(2)(9)(10)(7)
Momentum
Also there is the element of momentum and inertia in relativity. Momentum is like when one pushes an object. If we push a freely moving object then it will accelerate, and if the push is steady then it will go faster and faster, and if there is a great force pushing on the object then we expect the speed of the object to increase. So why can't anything go past the speed limit of the speed of light? Well the fact is that there is no possible way to create such a force to even reach the speed of light. Newtons 2nd Law has to do with momentum and
Inertia
Newton's first law of motion is known as the law of inertia, where inertia is a property of matter that opposes changes in velocity. Inertia causes a mass to stay at rest or in motion unless disturbed by another force. For example, if something is going at a steady and constant speed in a straight line, then it will not spontaneously change direction, speed up, or slow down on its own. The object would have to be disturbed by another force, and just like the inertia man, if it is standing still it will continue to do so. Inertia is the resistance in changes of motion. Let's say there is a small object and bigger heavier object. If the same amount of force is exerted on them, the bigger object's path of motion, it will be less affected than that of the small object. the difference between inertia and momentum is that inertia is a property of mass and does not change, and momentum is what changes as an object changes its velocity. We also have to remember that even though it takes pushes and pulls to change to change an object's velocity, it does not require pushes and pulls for the object to remain in motion, for the object has the ability to move on its own. Galileo is the first to consider this concept. He had formed the main theory of defining the causes of motion before Sir Issac Newton adapted his theory and finalized it by making it into a law. Lets say you are pushing a chair. It is automatically thought that when you stop pushing the chair, it will stop moving, but it was Galileo who believed that even as the force of your push is taken away from the chair, it will still maintain its velocity and continue to move across the room. Actually it is for certain that it will, but only if it is left alone (11)(12)
Equivalence of Mass and Energy
The more remarkable part of Albert Einstein's special theory of relativity is his conclusion that mass is merely a type of energy and is called the Law of Conservation of Mass-Energy. In his discoveries, Einstein found that energy equals mass multiplied by the speed of light squared. This equation is often his most well known and is written as E=mc2. Where E stands for energy, m and c stand for mass and the speed of light respectively. Mass that turns into forms of energy is just a tiny percentage of what is the total mass that is out of our sensory range. For example, if there is a chemical reaction, the mass and energy really appear to be conserved separately, but in a nuclear reaction the energy that is released is often around a million times greater than in a chemical one. In this the change in mass is easily measured.
Mass refers to the total number of atoms that make up any object that is composed of matter. Weight is the rate at which gravity exerts force on that mass and can fluctuate depending on the location, whereas mass is constant. There is a strong difference between enrgy and mass even though the two are closely related and often dependent on the other. Mass is tangible, you can see, pick up, and feel it; however, energy is more abstract . It is often defined as "the ability to do work". Even in an object with a small mass, there is a massive amount of energy. The Law of Conservation of Mass/Energy states that the two are interchangible. For example, mass can be turned into energy and visa-versa. It was this very principle that created the first nuclear bomb.
References
1. TriPod
2. The Physics Classroom (2)
3. Math Pages
4. Enriched Physics
5. Hyper Physics
6. Spiff
7. Virtual Vistitor Center
8. How Stuff Works
9. Physics Notes (LC)
10. Length Contraction
11. Mind
12. Man's Feild CT
13. Think Quest
14. Suite 101